So it'll turn to yet another arms race - similar to captcha, cybersecurity and nuclear weapons. SEO will use AI to fill in fluff inside AI-generated content (which is already done).
It won't directly match ChatGPT logs and OpenAI would just be pouring precious compute to a bottomless pit trying to partial-match.
Serve Claude-generated version to OpenAI bots. Serve OpenAI-generated version to Claude bots. Problem solved.
Serve users a random version and A/B test along the way.
Then you are still left with self hosted models which are pretty good at this task.